Your company, which is financed entirely with common equity, plans to manufacture a new product, a cell phone that can be worn like a wristwatch. Two robotic machines are available to make the phone, Machine A and Machine B. The price per phone will be $250.00 regardless of which machine is used to make it. The fixed and variable costs associated with the two machines are shown below, along with the capital (all equity) that must be invested to purchase each machine. The expected sales level is 25,000 units. Your company has tax loss carry-forwards that will cause its tax rate to be zero for the life of the project, so T = 0. How much higher or lower will the project's ROE be if you select the machine that produces the higher ROE, i.e., what is ROEB - ROEA? (Hint: Since the firm uses no debt and its tax rate is zero, ROE = EBIT/Required investment.)
A) 6.00%
B) 6.67%
C) 7.00%
D) 7.35%
E) 7.72%

Question

Quizplus · Accepted Answer

To determine which machine provides the higher ROE, we need to calculate the EBIT and required investment for each machine.

For Machine A:
- Variable cost per phone = $100.00
- Fixed cost = $500,000
- Capital investment = $2,000,000
- Total cost = (Variable cost per phone x Expected sales) + Fixed cost = ($100.00 x 25,000) + $500,000 = $2,750,000
- EBIT = Total revenue - Total cost = ($250.00 x 25,000) - $2,750,000 = $2,250,000
- Required investment = Capital investment = $2,000,000
- ROE = EBIT/Required investment = $2,250,000/$2,000,000 = 1.125 or 11.25%

For Machine B:
- Variable cost per phone = $125.00
- Fixed cost = $750,000
- Capital investment = $3,000,000
- Total cost = (Variable cost per phone x Expected sales) + Fixed cost = ($125.00 x 25,000) + $750,000 = $3,125,000
- EBIT = Total revenue - Total cost = ($250.00 x 25,000) - $3,125,000 = $1,875,000
- Required investment = Capital investment = $3,000,000
- ROE = EBIT/Required investment = $1,875,000/$3,000,000 = 0.625 or 6.25%

Therefore, ROEB - ROEA = 6.25% - 11.25% = -5.00%. This means that selecting Machine A would result in a higher ROE than selecting Machine B.

Best choice: Machine A.

Your Company, Which Is Financed Entirely with Common Equity, Plans